# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a260426 Showing 1-1 of 1 %I A260426 #24 Jul 28 2015 12:40:23 %S A260426 1,2,3,4,7,5,11,6,8,12,25,9,13,17,10,14,47,18,19,34,15,20,31,24,55,16, %T A260426 21,62,137,26,37,27,45,22,28,42,59,33,71,23,87,29,41,79,166,35,61,49, %U A260426 36,58,30,38,319,54,91,76,44,89,97,32,203,108,39,53,99,200,67,46,103,78,185,64,131,48,75,40,379,50,73,373,109,70,433,113,95,57,1123,111,143,121 %N A260426 a(1) = 1, a(A206074(n)) = A014580(a(n)), a(A205783(1+n)) = A091242(a(n)), where A014580 [respectively A091242] give binary codes for irreducible [resp. reducible] polynomials over GF(2), while A206074 and A205783 give similar codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q. %C A260426 Each term of A260427 resides in a separate infinite cycle. This follows because any polynomial with (coefficients 0 or 1) that is irreducible over GF(2) is also irreducible over Q, in other words, A014580 is a subset of A206074. [See _Thomas Ordowski_'s Feb 21 2014 comment in A014580] and thus any term of A091242 in A206074 is trapped into a trajectory containing only terms of A014580. %H A260426 Antti Karttunen, Table of n, a(n) for n = 1..7968 %H A260426 Index entries for sequences that are permutations of the natural numbers %F A260426 a(1) = 1; for n > 1, if A257000(n) = 1 [when n is in A206074], then a(n) = A014580(a(A255574(n))), otherwise [when n is in A205783], a(n) = A091242(a(A255572(n))). %F A260426 As a composition of related permutations: %F A260426 a(n) = A246202(A260421(n)). %F A260426 a(n) = A245703(A260424(n)). %o A260426 (PARI) %o A260426 allocatemem(234567890); %o A260426 vecsize = (2^24)-4; %o A260426 uplim = 2^25; %o A260426 v014580 = vector(vecsize); A014580 = n -> v014580[n]; %o A260426 v091242 = vector(vecsize); A091242 = n -> v091242[n]; %o A260426 v255574 = vector(vecsize); A255574 = n -> v255574[n]; %o A260426 A255572 = n -> (n - A255574(n) - 1); %o A260426 isA014580(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from _Charles R Greathouse IV_ %o A260426 isA206074(n) = polisirreducible(Pol(binary(n))); %o A260426 A257000 = n -> isA206074(n); %o A260426 v255574[1] = 0; i=0; j=0; n=2; while((n < uplim), if(!(n%65536),print1(n,", ")); v255574[n] = v255574[n-1]+A257000(n); if(isA014580(n), i++; v014580[i] = n, j++; v091242[j] = n); n++); print(n); %o A260426 A260426(n) = if(1==n, 1, if(isA206074(n), A014580(A260426(A255574(n))), A091242(A260426(A255572(n))))); %o A260426 for(n=1, 7968, write("b260426.txt", n, " ", A260426(n))); %Y A260426 Inverse: A260425. %Y A260426 Related permutations: A246202, A245703, A260421, A260424. %Y A260426 Cf. A014580, A091242, A205783, A206074, A257000, A255572, A255574, A260427. %Y A260426 Differs from A245703 for the first time at n=25, where a(25)=55, while A245703(25)=16. %K A260426 nonn,look %O A260426 1,2 %A A260426 _Antti Karttunen_, Jul 26 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE